Pseudo-random sequence padding in an OFDM modulation system

ABSTRACT

A method of estimating timing of at least one of the beginning and the end of a transmitted signal segment in the presence of time delay in a signal transmission channel. Each of a sequence of signal frames is provided with a pseudo-noise (PN) m-sequences, where the PN sequences satisfy selected orthogonality and closures relations. A convolution signal is formed between a received signal and the sequence of PN segments and is subtracted from the received signal to identify the beginning and/or end of a PN segment within the received signal. PN sequences are used for timing recovery, for carrier frequency recovery, for estimation of transmission channel characteristics, for synchronization of received signal frames, and as a replacement for guard intervals in an OFDM context.

FIELD OF THE INVENTION

This invention relates to electronic communication of messages, and moreparticularly to communication of information for Internet, digitaltelevision, data broadcasting and other wideband applications.

BACKGROUND OF THE INVENTION

Transmission of Internet signals and of digital television (TV) signalsposes different but continuing challenges for each activity. Internetsignal transmission faces the problems of reliable broadcasting andmulticasting of messages, provision of mobility for signal transmitterand for recipient, and limitations on information transfer rate(“speed”). Transmission of digital TV signals faces the problems ofproviding an interactive system, providing point-to-point informationtransfer capacity, and mobility of the recipient. The system should beefficient in the sense that the payload or data portion of eachtransmitted frame is a large fraction of the total frame. At the sametime, the system should be able to identify, and compensate for, varyingcharacteristics of the transmission channel, including but not limitedto time delay associated with transmission of each frame.

What is needed is a system that provides timing recovery, carrierrecovery and estimation of channel characteristics associated withsignal propagation in a channel, and that also serves as a guardinterval and as a frame synchronizer for the transmitted signal.

SUMMARY OF THE INVENTION

The invention meets these needs by providing a pseudo-random orpseudo-noise (PN) sequence for each transmitted frame, where the PNsequence satisfy certain orthogonality and closure relations withrespect to algebraic operations such as convolution, Boolean additionand position shift within a segment. A convolution signal is formedbetween a received signal (transmitted through a channel) and one ormore of a selected sequence of the PN sequences. This convolution signalis analyzed to identify the beginning or end of a PN sequence, toidentify time delay in the channel, and to permit timing recovery. Acarrier frequency for the received signal can be recovered from thesignal symbols (bit, nibbles, bytes, etc.) that make up the PNsequences, and synchronization of signal frames can be implemented.Characteristics of the transmission channel can be estimated from thetime delays and associated phase shifts. A PN sequence can be positionedwithin a signal frame to serve as a guard interval for an orthogonalfrequency, multiple carrier modulation (“OFDM”) scheme. Taken together,these features allow demodulation of a transmitted signal within an OFDMscheme.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B illustrate alternative formats for an OFDM framesequence.

FIGS. 2A, 2B and 2C illustrate alternative formats for incorporating aPN sequence according to the invention.

FIG. 3 illustrates a set of PN sequences that can be formed within aframe sync segment.

FIG. 4 illustrates a representative transmitted signal.

FIGS. 5A and 5B illustrate non-overlapping components of an idealizedsequence of signal frames.

FIGS. 6A and 6B illustrate the incremental effects of a representativemultipath (dotted lines) on a sequence of modified frame sync segments.

FIG. 7 is a flow chart of a procedure for practising the invention.

FIGS. 8 and 9 illustrate a transmitter system and a receiver system thatcan be used to practice the invention.

DESCRIPTION OF BEST MODES OF THE INVENTION

An OFDM format for a signal in first and second configurations is shownin FIGS. 1A and 1B. In the format of FIG. 1A, a DFT (or FFT) block 11Ais preceded by a cyclic prefix segment 13A that serves as a guardinterval for the DFT block. Use of a guard interval, or its equivalent,is required with an OFDM format, in order to account for the possiblepresence of multipath signals in a received signal. In the format ofFIG. 1B, a DFT block is followed by a zero-padding segment that alsoserves as a guard interval for the DFT block.

A pseudo-random or pseudo-noise (PN) sequence, a coded m-sequence ofsymbols, is used in an OFDM format. An m-sequence is a sequence ofsymbols, usually 0's and 1's, of a selected length that satisfies threerequirements: (1) the number of symbols of different types (e.g., thenumber of 0's and the number of 1's) is “balanced”, or approximately thesame, over the set of such sequences; (2) the Boolean sum of any twom-sequences, and the result of end-around shifting of symbols in anym-sequence, is again an m-sequence; and (3) the convolution of twom-sequences, MS(t;i) and MS(t;j), satisfies an orthogonality condition:MS(t+Δt;i)*MS(t;j)=δ(Δt)·δ(i,j),  (1)where δ(Δt) is a modified delta function (δ(Δt)=0 for |Δt|>Δt1) andδ(i,j) is a Kronecker delta (=0 unless i=j). The Kronecker delta can beomitted if the m-sequence is independent of the index number i, or ifthe index numbers are known to satisfy i=j. The length of an m-sequenceis most conveniently chosen to be 2^(J)−1, where J is a selectedpositive integer, such as J=7, 8 or 9.

A subset of the set of all m-sequences, referred to as coded m-sequencesand denoted PN(t;i) for an index number i, are of interest. A set of(coded) PN sequences may be generated using Walsh sequence coding orusing a similar Haar sequence coding. Techniques for generating Walshcodes or Haar codes are discussed in T. J. Lynch, Data Compression, VanNostrand, New York, 1985, pp. 79–85, and in V. J. Garg, K. Smolik and J.E. Wilkes, Applications of CDMA in Wireless/Personal Communications,Prentice Hall, Upper Saddle River, N.J., 1997, pp. 23–39. Other sets ofPN sequences, satisfying Eq. (1), can be generated and used as well.

A PN sequence is a Mth order m-sequence that can be implemented by aFibonacci-type linear feedback shift register (LFSR) that is well knownin the art. One suitable characteristic polynomial, associated with theLFSR and used for the choice M=9, isp(x;4;9)=1+x ⁴ +x ⁹.  (2)An initial condition mask, applied to the LFSR, determines the initialcondition of, and thus the phase of, a PN sequence that is generated.Any other suitable characteristic polynomial can be used here,consistent with the choice of order M.

In a first embodiment, illustrated in FIG. 2A, a coded PN sequence 23Ais included in, or replaces, the cyclic prefix segment 13A shown in FIG.1A and is associated with the DFT block 21A. In a second embodiment,illustrated in FIG. 2B, a coded PN sequence 23B is included in, orreplaces, the zero padding segment 13B shown in FIG. 1B and isassociated with the DFT block 21B.

In a third embodiment, illustrated in FIG. 2C, a coded PN sequence 23Cis associated with, and included in, a frame sync segment 25C thatprecedes and is associated with a DFT block 21C. The frame sync segmentoptionally includes a preamble 24C that immediately precedes the PNsequence 23C and optionally includes a post-amble 26C that immediatelyfollows the PN sequence. The lengths of the preamble, the PN sequenceand the post-amble are F1, F2 and F3, respectively, where F1 and F3 areselected non-negative integers and F2 is a selected positive integer.The frame sync segment has a length F1+F2+F3 symbols.

In the format shown in FIG. 2C, the preamble and post-amble segments arenot chosen arbitrarily. Preferably, the preamble and post-amble symbolsare chosen so that any ordered set of F2 consecutive symbols from theframe sync segment (of length F1+F2+F3) is also a PN sequence; moreparticularly, a PN sequence formed by a selected number of end-aroundshifts of the “original” PN sequence located at positions number F1+1through number F1+F2 in the frame sync segment, as illustrated in FIG.3. The frame sync segment, if present in the signal frame, may becharacterized by an associated PN sequence (e.g., the “original” PNsequence indicated in FIG. 3).

The information transfer unit used here is a signal frame, whichincludes the frame body 21A or 21B in the format shown in FIGS. 2A and2B, or includes the frame sync segment 26C and the frame body 21C in theformat shown in FIG. 2C. The frame body, 21A or 21B or 21C, includes aDFT block with a header having a fixed number of signal symbols (octets,bytes, nibbles or bits) that provide information on the frame source,frame destination, sequence number, frame window size, if any, data type(supervisory, information, unnumbered), data payload size, flow control,message priority, error detection and correction checksum, and othersupervisory information (referred to collectively as the “header”), plusthe data payload itself, which preferably has a fixed size, or may havea prescribed range of sizes.

Let Tr(t) be a signal representing a sequence of transmitted signalframes, as illustrated in FIG. 4. A signal frame is identified byisolating and analyzing an associated PN sequence, which requiresprecise knowledge of where each PN sequence begins and ends within asequence of signal frames.

A sequence of idealized modified signal frames can be decomposed intotwo non-overlapping sequences: a first sequence S1 of PN sequencesPN(t;i;ideal), and a second sequence S2 of DFT blocks DFT(t;i;ideal), asillustrated in FIGS. 5A and 5B.

However, each transmitted signal frame is subject to signal time delay,including multipath signal degradation, and reasonably precise timing isrequired in order to distinguish a PN sequence from any other segmentwithin a signal frame. FIGS. 6A and 6B illustrate the incrementaleffects of a representative multipath signal mp(t) (dotted lines) on asequence of modified frame sync segments and on a sequence of modifiedDFT segments that are split apart as illustrated. Although eachidealized modified PN sequence PN(t;i;ideal) decreases abruptly to 0 att=t″(i), the received sequence PN(t;i;Rc) decreases to 0 slowly within atime interval t″(i)≦t≦t′″(i)<t′(i+1), as illustrated in FIG. 6A. In asimilar manner, although idealized DFT block DFT(t;i;ideal) decreases to0 abruptly at t=t′(i+1), the received block DFT(t;i;Rc) decreases to 0slowly within a time interval t′(i+1)≦t≦t″“(i+1)<t”(i+1), as illustratedin FIG. 6B. It is thus difficult to locate the times, t=t′(i;Rc) andt=t″(i;Rc), at the receiver, corresponding to the beginning and end of aPN sequence that would be received without multipath.

Let h(t) be a response to transmission of an impulse signal δ(t)(modified delta function with infinitesimal width Δt1) along thetransmission channel TC used for a signal frame. If the sign Tr(t) istransmitted along the channel TC, a receive signal Rc(t) may beexpressed as a convolution of the transmitted signal and the impulseresponse signal,Rc(t2)=Tr(t1)*h(t2−t1),  (3)Tr(t)=PN(t;i;ideal)+mp(t)(t=(i;Rc)≦t<t′(i+1;Rc),  (4)where * indicates that a convolution or correlation operation isperformed on the two signals Tr(t1) and h(t2−t1). Because of theorthogonal construction of each PN sequence in Eq. (1), one verifiesthatPN(t+Δt;i;ideal)*PN(t;j;ideal)=δ(Δt)·δ(i,j)  (5)PN(t+Δt;i;ideal)*Rc(t)=δ(Δt)*h(t)+(small residual due to mp(t))  (6)within a time interval t′(i;Rc)≦t≦t″(i;Rc), where the Kronecker deltaindex δ(i,j) (=0 or 1) can be dropped if the PN sequences PN(t;i;ideal)are independent of the index i, or if the particular PN sequence (i) isknown and i=j.

Where the sequence PN(t;i;ideal) is known and the impulse response h(t)is measurable, and thus known, for the channel TC, the convolutionsignal formed in Eq. (6) can be used to determine time points(t=t′(i;Rc) and t=t″(i;Rc)) corresponding to the “edges” of theidealized PN signal, as received at the receiver after transmissionthrough the channel TC. Segments of the received signal, defined byRc(t;i)=Rc(t) (t′(i;Rc)≦t≦t″(i;Rc))=0 (other values of t),  (7)can thus be concatenated to form a composite signalk2Rc(t; Δt;comp)=ΣPN(t+Δt;k)*Rc(t;i),k=k1  (8)where k1 and k2 (≧k1) are selected integers for the sequence of signalframes analyzed. The composite signal Rc(t; Δt;comp)) is then subtractedfrom the received signal Rc(t) to obtain the remainder signalRc(t;rem)=Rc(t)−Rc(t; Δt;comp),  (9)which explicitly exhibits the effects of multipath on the receivedsignal in each of the time intervals t″(i;Rc)≦t≦t′(i+1;Rc). From thismultipath information, one can identify the beginning and end of each(time delayed) DFT block and the corresponding PN sequence, and thusidentify a signal frame within a sequence of signal frames.

After the time delay associated with a received frame is determined orestimated, signal carrier frequency can be recovered and frequency shiftand/or frequency drift can be estimated, using the known symbol patternincorporated in a PN sequence associated with the signal frame.

One or more transmission channel characteristics can be estimated,frame-by-frame or over a group of frames, using a knowledge of timedelay and frequency shift and/or frequency drift for the frame(s).

In the frequency domain, a signal frame has an associated bandwidth Δf1.Adequate coverage of this bandwidth without producing an alias signalrequires that the sampling rate in the time domain for a DFT block andfor its associated PN sequence be at least equal to the Nyquist rate. Insome instances, this may require a sampling rate greater than the symbolrate for the signal frame.

The delta function produced by the convolution operation in Eq. (1) hasa very small, but non-zero, temporal width Δt1, and provision of asignal having this width in the time domain requires use of acorresponding bandwidth Δf2 in the frequency domain. The actualbandwidth Δf1 provided for the signal frame should be at least equal tothe required bandwidth Δf2.

One method of estimating one or more transmission channelcharacteristics analyzes the Fourier transform FT(f;Rc) of a receivedsignal Rc(t) corresponding to transmission of an impulse function h(t).Ideally, the Fourier transform FT(f;Rc) is approximately a syncfunction,FT(f;Rc;ideal)=sync(f/f0),  (10)with an appropriate choice of a reference frequency f0 representing thebandwidth in the Fourier domain. The deviation of the actual Fouriertransform FT(f;Rc) from the ideal transform FT(f,Rc;ideal) can be usedto estimate one or more (time varying) characteristics for thetransmission channel, frame by frame or over a sequence of frames, asdesired.

Once the time delay associated with a PN sequence (associated with asignal frame) is determined and compensated for, the PN sequence can beused to synchronize its associated signal frame.

In any of the formats shown in FIGS. 2A, 2B and 2C, when time delayassociated with a frame has been determined or estimated, the PNsequence can serve as a guard interval for the DFT block because (1) thesymbol sequence associated with the PN sequence is known and (2) thebeginning time and/or ending time for the PN sequence is known. Thus, noadditional guard interval within the frame body need be provided. Thedata payload portion of the frame body may be increased to include theformer guard interval and/or the frame body length can be reduced by thelength of a guard interval that would otherwise be provided in aconventional approach. The information developed in the preceding alsoallows demodulation of the received signal.

Insertion and analysis of a PN sequence in each transmitted signal frameallows the following: (1) recovery of timing, frame by frame if desired,and estimation of multipath signal degradation; (2) recovery of carrierfrequency; (3) estimation of one or more transmission channelparameters; (4) deletion of a guard interval that serves only as a guardinterval; and (5) synchronization of each signal frame received.

FIG. 7 is a flow chart of a procedure for estimating timing of at leastone of the beginning and the end of a transmitted signal segment in thepresence of time delay in the signal transmission channel in an OFDMsystem, according to the invention. In step 71, a set of K (≧1)pseudo-random m-sequences PN(t;k) are provided that satisfy convolutionsignal orthogonality, as in Eq. (1) or (5). In step 72, a selectedsequence is appended to at least one signal frame to form a paddedsignal frame. In step 73, at least one padded signal frame istransmitted through a transmission channel having an uncontrollablesignal time delay. In step 74, a received version Rc(t) of thetransmitted signal is received, and a sum Rc(t;Δt;comp) of convolutionsignals PN(t+Δt;k)*Rc(t;i) is formed, as in Eq. (8), for k1≦k≦k2. Instep 75, a remainder signal Rc(t;rem)=Rc(t)−Rc(t;Δt;comp) is formed. Asin Eq. (9). In step 76, the remainder signal is analyzed to determine atleast one time at which at least one of the sequences PN(t;k) begins orends in the received signal Rc(t).

FIG. 8 schematically illustrates a transmitter system 80 that can beused to practice the invention. Data are received at a DFT (or FFT)converter block 81 and converted to an appropriate digital format. A PNsequence(s) module 83 provides one or more PN sequences to be used withsignal frames containing the DFT information. Output signals from theDFT block 81 and from the PN Sequence(s) block 83 are received at amultiplexer (MUX) 85 and are issued as a MUX output signal containingalternating segments of DFT blocks and PN sequences. The MUX outputsignal is received and processed by an RF module 87, and the resultingsignal is sent to, and transmitted by, an antenna or other signaltransmitter 89.

FIG. 9 schematically illustrates a receiver system 90 that can be usedto practice the invention. A data-carrying (modulated) signal isreceived at an antenna or other signal receiver 91 and is initiallysubjected to frequency downconversion by a downconverter module 93. Adownconverted signal frame, including a DFT block and an appended PNsequence, is received at a PN sequence processor 95 that performs timingrecovery, carrier recovery (optional), channel estimation (optional) andframe synchronization (optional) to provide channel state information.The downconverted signal frame is also received at a PN sequence removalmodule 97. After the PN sequence processor 95 has performed its task(s),the processor issues a control signal that is received by the PNsequence removal module 97, the appended PN sequence is removed from thesignal frame, and the resulting DFT block is sent to a DFT conversionmodule 99. The converted DFT portion of the original signal frame issuesas a demodulated signal (data). Channel state information obtained fromanalysis of the PN sequence issues from the PN sequence processor 95.Optionally, each received signal frame is analyzed separately todetermine the channel state information.

1. A method of estimating timing of at least one of the beginning andthe end of a transmitted signal segment in the presence of time delay ina signal transmission channel in an OFDM system, the method comprising:providing a set of pseudo-random signal m-sequences PN(t;k) (k=1, . . ., K; K≧1) for which a convolution signal formed from any two sequencessatisfies PN(t;i)*PN(t+Δt;j)=δ(Δt)·δ(i,j), where i and j are indexnumbers identifying the two sequences, t is a time variable, δ(Δt) is amodified delta function with infinitesimal width Δt1 (δ(Δt)=0 for|Δt|>Δt1) and δ(i,j)=0 unless i=j; appending a selected sequence PN(t;k)from the set of pseudo-random signal m-sequences PN(t;k) to at least onesignal frame to be transmitted to form a padded signal frame;transmitting at least one padded signal frame as the transmitted signalthrough the signal transmission channel in which the transmitted signalmay be received with an uncontrollable time delay Δt(delay); receiving areceived signal Rc(t) of the transmitted signal associated with the atleast one padded signal frame being transmitted and forming a compositesignal, denoted as Rc(t; Δt;comp), given as:${{R\;{c\left( {t;{\Delta\; t};{comp}} \right)}} = {\sum\limits_{k = {k\; 1}}^{k\; 2}\;{{{PN}\left( {{t + {\Delta\; t}};k} \right)}*R\;{c(t)}}}},$where Δt is a selected time increment and k1 and k2 satisfy 1≦k1≦k2≦K;forming a remainder signal, denoted as Rc(t;rem), whereRc(t;rem)=Rc(t)−Rc(t;Δt;comp); and determining from the remainder signalat least one time at which said selected sequence PN(t;k) (k=k1, k1+1, .. . , k2) associated with said at least one padded signal frame beginsin the received signal Rc(t).
 2. The method of claim 1, furthercomprising determining a carrier frequency associated with said selectedsequence PN(t;k) of the at least one padded signal frame beingtransmitted.
 3. The method of claim 1, further comprising using at leastone of the selected sequences PN(t;k) associated with the padded signalframes being transmitted to estimate at least one parameter associatedwith said signal transmission channe.
 4. The method of claim 1, furthercomprising replacing at least one guard interval associated with atleast one of said signal frames to be transmitted with a selected one ofthe m-sequences PN(t;k).
 5. The method of claim 1, further comprisingusing at least one of the selected sequences PN(t;k), associated withone of said padded signal frames being transmitted, to provide timesynchronization for said associated padded signal frame.